IMPORTANT: Please make sure you create a copy of this file with a customized name, so that your work (e.g. answers to the questions) is not over-written when you pull the latest content from the course github.

The purpose of this exercise is to become familiar with:

  1. Some time series analysis tools;
  2. Correlation matrices and principal component analysis (PCA) (see readings of sessions 3-4);
  3. More data manipulation and reporting tools (including Google Charts).

As always, while doing this exercise we will also see how to generate replicable and customizable reports. For this purpose the exercise uses the R Markdown capabilities (see Markdown Cheat Sheet or a basic introduction to R Markdown). These capabilities allow us to create dynamic reports. For example today’s date is 2017-05-16 (you need to see the .Rmd to understand that this is not a static typed-in date but it changes every time you compile the .Rmd - if the date changed of course).

Before starting, make sure you have pulled the exercise set 2 souce code files on your github repository (if you pull the course github repository you also get the exercise set files automatically). Moreover, make sure you are in the directory of this exercise. Directory paths may be complicated, and sometimes a frustrating source of problems, so it is recommended that you use these R commands to find out your current working directory and, if needed, set it where you have the main files for the specific exercise/project (there are other ways, but for now just be aware of this path issue). For example, assuming we are now in the “Data Analytics R version/INSEADAnalytics” directory, we can do these:

getwd()
setwd("Exercises/Exerciseset2/")
list.files()

Note: as always, you can use the help command in Rstudio to find out about any R function (e.g. type help(list.files) to learn what the R function list.files does).

Let’s now see the exercise.

IMPORTANT: You should answer all questions by simply adding your code/answers in this document through editing the file ExerciseSet2.Rmd and then clicking on the “Knit HTML” button in RStudio. Once done, please post your .Rmd and html files in your github repository.

The Exercise: Introduction

For this exercise we will use the Futures’ daily returns to develop what is considered to be a “classic” hedge fund trading strategy, a futures trend following strategy. There is a lot written about this, so it is worth doing some online search about “futures trend following”, or “Managed Futures”, or “Commodity Trading Advisors (CTA)”. There is about $300 billion invested on this strategy today, and is considered to be one of the oldest hedge fund strategies. Some example links are:

Of course there are also many starting points for developing such a strategy (for example this R bloggers one (also on github), or the turtle traders website which has many resources.

In this exercise we will develop our own strategy from scratch.

Note (given today’s market conditions): Prices of commodities, like oil or gold, can be excellent indicators of the health of the economy and of various industries, as we will also see below.

Getting the Futures Data

There are many ways to get futures data. For example, one can use the Quandl package, or the turtle traders resources, or (for INSEAD only) get data from the INSEAD library finance data resources website. One has to pay attention on how to create continuous time series from underlying contracts with varying deliveries (e.g. see here ). Using a combination of the resources above, we will use data for a number of commodities.

Data description

Let’s load the data and see what we have.

suppressPackageStartupMessages(source("helpersSet2.R"))
load("data/FuturesTrendFollowingData.Rdata")

We have data from 2001-01-02 to 2015-09-24 of daily returns for the following 64 futures:

print(colnames(futures_data))
##  [1] "Corn"               "Wheat"              "Soybeans"          
##  [4] "Soybean Oil"        "Soybean Meal"       "Lean Hoggs"        
##  [7] "Sugar"              "Coffee"             "Cocoa"             
## [10] "Cotton"             "Canola"             "Orange Juice"      
## [13] "Lumber"             "Natural Gas"        "Crude Oil"         
## [16] "Brent Crude"        "Heating Oil"        "Kerosene"          
## [19] "Gas Oil"            "Gasoline"           "Copper NY"         
## [22] "Copper LDN"         "Silver"             "Gold"              
## [25] "Platinum"           "Palladium"          "Aluminium"         
## [28] "Zinc"               "Nickel"             "Treasury Bonds"    
## [31] "5 yr T-Notes US"    "2 yr T-Note US"     "10yr T-Notes"      
## [34] "Euro-Bund"          "Euro-Bobl"          "Euro-Schatz"       
## [37] "Canadian Bond"      "JGB Japan"          "Gilts UK"          
## [40] "Euroyen"            "Eurodollar"         "Euroswiss"         
## [43] "Euribor"            "SP500 E-Mini"       "DAX 30"            
## [46] "Eurostoxx"          "Hang Seng"          "FTSE 100 UK"       
## [49] "Nasdaq 100 Mini"    "Russel 2000 E-Mini" "Dow Jones"         
## [52] "TSE Toronto"        "CAC 40 France"      "OMX 30 Stockholm"  
## [55] "NIKKEI 225"         "Euro"               "Norwegian Krone"   
## [58] "New Zealand Dollar" "Australian Dollar"  "British Pound"     
## [61] "Canadian Dollar"    "Swiss Franc"        "Japanese Yen"      
## [64] "Singapore Dollar"

Basic data analysis

Let’s see how these are correlated. The correlation matrix is as follows:

Corn Wheat Soybeans Soybean Oil Soybean Meal Lean Hoggs Sugar Coffee Cocoa Cotton Canola Orange Juice Lumber Natural Gas Crude Oil Brent Crude Heating Oil Kerosene Gas Oil Gasoline Copper NY Copper LDN Silver Gold Platinum Palladium Aluminium Zinc Nickel Treasury Bonds 5 yr T-Notes US 2 yr T-Note US 10yr T-Notes Euro-Bund Euro-Bobl Euro-Schatz Canadian Bond JGB Japan Gilts UK Euroyen Eurodollar Euroswiss Euribor SP500 E-Mini DAX 30 Eurostoxx Hang Seng FTSE 100 UK Nasdaq 100 Mini Russel 2000 E-Mini Dow Jones TSE Toronto CAC 40 France OMX 30 Stockholm NIKKEI 225 Euro Norwegian Krone New Zealand Dollar Australian Dollar British Pound Canadian Dollar Swiss Franc Japanese Yen Singapore Dollar
Corn 1.00 0.63 0.60 0.51 0.52 0.02 0.21 0.17 0.10 0.23 0.45 0.06 0.08 0.12 0.24 0.25 0.22 0.02 0.15 0.25 0.23 0.22 0.23 0.18 0.13 0.17 0.20 0.18 0.16 -0.08 -0.07 -0.05 -0.07 -0.08 -0.06 -0.08 -0.07 -0.03 -0.06 -0.01 -0.01 -0.05 -0.07 0.14 0.13 0.13 0.08 0.16 0.10 0.12 0.11 0.18 0.13 0.15 0.05 0.17 0.20 0.18 0.21 0.16 -0.20 0.11 -0.02 0.17
Wheat 0.63 1.00 0.45 0.42 0.39 0.03 0.20 0.18 0.09 0.22 0.38 0.03 0.07 0.09 0.21 0.21 0.18 0.00 0.12 0.21 0.21 0.21 0.20 0.16 0.12 0.15 0.17 0.17 0.14 -0.10 -0.09 -0.07 -0.09 -0.07 -0.06 -0.06 -0.07 -0.02 -0.06 -0.01 -0.04 -0.06 -0.06 0.13 0.13 0.13 0.06 0.15 0.10 0.13 0.11 0.17 0.13 0.13 0.05 0.16 0.20 0.18 0.20 0.15 -0.20 0.12 0.00 0.16
Soybeans 0.60 0.45 1.00 0.74 0.84 0.04 0.20 0.16 0.12 0.26 0.64 0.08 0.08 0.11 0.27 0.27 0.25 0.04 0.18 0.28 0.28 0.26 0.24 0.17 0.17 0.21 0.23 0.21 0.18 -0.12 -0.11 -0.09 -0.11 -0.11 -0.10 -0.10 -0.09 -0.02 -0.12 -0.02 -0.05 -0.09 -0.09 0.15 0.17 0.17 0.13 0.20 0.11 0.14 0.13 0.20 0.18 0.20 0.08 0.17 0.22 0.19 0.25 0.17 -0.22 0.11 -0.01 0.21
Soybean Oil 0.51 0.42 0.74 1.00 0.47 0.04 0.20 0.18 0.13 0.28 0.64 0.10 0.09 0.13 0.34 0.34 0.31 0.09 0.25 0.37 0.32 0.30 0.29 0.23 0.20 0.24 0.27 0.25 0.22 -0.14 -0.12 -0.09 -0.12 -0.11 -0.10 -0.11 -0.10 -0.02 -0.13 0.00 -0.04 -0.08 -0.08 0.20 0.20 0.20 0.19 0.25 0.14 0.19 0.18 0.24 0.22 0.24 0.12 0.20 0.26 0.24 0.30 0.21 -0.28 0.13 -0.05 0.23
Soybean Meal 0.52 0.39 0.84 0.47 1.00 0.02 0.16 0.13 0.09 0.20 0.51 0.08 0.07 0.09 0.17 0.17 0.16 0.02 0.11 0.17 0.20 0.18 0.17 0.12 0.12 0.15 0.16 0.15 0.13 -0.08 -0.08 -0.07 -0.08 -0.07 -0.07 -0.07 -0.06 -0.02 -0.08 -0.01 -0.04 -0.07 -0.07 0.10 0.13 0.13 0.09 0.15 0.08 0.09 0.09 0.15 0.13 0.15 0.07 0.13 0.16 0.15 0.19 0.12 -0.17 0.08 0.01 0.16
Lean Hoggs 0.02 0.03 0.04 0.04 0.02 1.00 0.03 0.02 0.03 0.02 0.01 0.01 0.03 0.04 0.07 0.06 0.05 -0.02 0.02 0.05 0.06 0.06 0.02 0.01 0.05 0.04 0.05 0.07 0.06 -0.04 -0.05 -0.04 -0.04 -0.04 -0.03 -0.02 -0.04 0.01 -0.05 0.00 -0.05 -0.05 -0.04 0.04 0.04 0.06 0.01 0.06 0.01 0.02 0.03 0.05 0.06 0.04 0.02 0.00 0.01 0.01 0.02 0.02 -0.03 -0.02 -0.03 0.01
Sugar 0.21 0.20 0.20 0.20 0.16 0.03 1.00 0.22 0.15 0.19 0.17 0.06 0.04 0.07 0.20 0.19 0.17 0.02 0.14 0.19 0.23 0.21 0.18 0.13 0.12 0.16 0.19 0.18 0.16 -0.07 -0.06 -0.04 -0.06 -0.09 -0.10 -0.09 -0.05 0.00 -0.08 0.00 -0.01 -0.04 -0.06 0.11 0.12 0.13 0.08 0.15 0.08 0.11 0.08 0.13 0.13 0.14 0.08 0.13 0.15 0.17 0.20 0.13 -0.15 0.09 -0.04 0.16
Coffee 0.17 0.18 0.16 0.18 0.13 0.02 0.22 1.00 0.18 0.16 0.12 0.06 0.07 0.05 0.15 0.14 0.13 0.04 0.12 0.15 0.19 0.18 0.20 0.15 0.13 0.17 0.17 0.17 0.15 -0.06 -0.05 -0.03 -0.05 -0.06 -0.06 -0.06 -0.05 0.00 -0.05 -0.01 -0.01 -0.05 -0.04 0.12 0.13 0.13 0.11 0.13 0.07 0.12 0.11 0.14 0.13 0.14 0.07 0.15 0.17 0.19 0.20 0.15 -0.17 0.08 0.00 0.16
Cocoa 0.10 0.09 0.12 0.13 0.09 0.03 0.15 0.18 1.00 0.12 0.08 0.05 0.06 0.04 0.16 0.15 0.13 0.06 0.15 0.14 0.17 0.17 0.21 0.18 0.13 0.14 0.16 0.16 0.12 -0.08 -0.06 -0.02 -0.07 -0.10 -0.09 -0.06 -0.07 -0.01 -0.09 -0.03 -0.01 -0.05 -0.05 0.10 0.11 0.12 0.12 0.11 0.06 0.11 0.09 0.13 0.13 0.14 0.07 0.21 0.22 0.22 0.23 0.24 -0.20 0.14 0.01 0.19
Cotton 0.23 0.22 0.26 0.28 0.20 0.02 0.19 0.16 0.12 1.00 0.22 0.08 0.07 0.04 0.20 0.20 0.18 0.03 0.16 0.19 0.23 0.22 0.17 0.13 0.10 0.15 0.19 0.18 0.18 -0.10 -0.10 -0.08 -0.10 -0.09 -0.09 -0.10 -0.08 -0.02 -0.08 0.01 -0.06 -0.07 -0.07 0.17 0.16 0.17 0.09 0.18 0.13 0.16 0.15 0.18 0.17 0.17 0.05 0.17 0.20 0.17 0.21 0.15 -0.20 0.11 -0.01 0.17
Canola 0.45 0.38 0.64 0.64 0.51 0.01 0.17 0.12 0.08 0.22 1.00 0.06 0.06 0.06 0.17 0.19 0.16 0.03 0.11 0.21 0.18 0.16 0.18 0.13 0.12 0.15 0.15 0.14 0.12 -0.09 -0.09 -0.07 -0.08 -0.06 -0.07 -0.09 -0.05 -0.02 -0.07 -0.01 -0.05 -0.06 -0.09 0.09 0.10 0.10 0.11 0.13 0.07 0.07 0.07 0.16 0.11 0.13 0.06 0.09 0.13 0.11 0.15 0.10 -0.06 0.05 -0.02 0.12
Orange Juice 0.06 0.03 0.08 0.10 0.08 0.01 0.06 0.06 0.05 0.08 0.06 1.00 0.04 0.05 0.10 0.08 0.08 0.04 0.08 0.09 0.09 0.08 0.10 0.06 0.06 0.07 0.10 0.07 0.08 -0.05 -0.03 -0.02 -0.04 -0.06 -0.06 -0.06 -0.07 -0.03 -0.06 -0.02 -0.01 -0.02 -0.04 0.08 0.08 0.09 0.07 0.10 0.06 0.06 0.08 0.10 0.08 0.11 0.07 0.06 0.05 0.07 0.09 0.03 -0.09 0.03 -0.03 0.07
Lumber 0.08 0.07 0.08 0.09 0.07 0.03 0.04 0.07 0.06 0.07 0.06 0.04 1.00 0.00 0.07 0.07 0.07 0.04 0.05 0.09 0.12 0.11 0.07 0.02 0.03 0.06 0.10 0.08 0.09 -0.10 -0.11 -0.09 -0.11 -0.08 -0.08 -0.07 -0.09 0.01 -0.10 -0.01 -0.07 -0.08 -0.06 0.12 0.14 0.14 0.08 0.14 0.12 0.10 0.11 0.10 0.14 0.12 0.04 0.05 0.08 0.09 0.11 0.08 -0.09 0.01 -0.07 0.09
Natural Gas 0.12 0.09 0.11 0.13 0.09 0.04 0.07 0.05 0.04 0.04 0.06 0.05 0.00 1.00 0.29 0.27 0.34 0.00 0.20 0.16 0.10 0.09 0.08 0.07 0.04 0.06 0.09 0.06 0.05 -0.02 -0.02 -0.02 -0.02 0.00 0.00 0.01 -0.02 -0.01 -0.01 0.00 -0.01 -0.01 0.00 0.04 0.04 0.03 0.03 0.04 0.02 0.03 0.03 0.10 0.04 0.04 0.03 0.07 0.07 0.07 0.09 0.06 -0.10 0.06 0.01 0.05
Crude Oil 0.24 0.21 0.27 0.34 0.17 0.07 0.20 0.15 0.16 0.20 0.17 0.10 0.07 0.29 1.00 0.89 0.84 0.10 0.56 0.66 0.37 0.35 0.29 0.26 0.20 0.24 0.30 0.27 0.25 -0.20 -0.14 -0.10 -0.17 -0.15 -0.14 -0.12 -0.15 -0.02 -0.14 -0.03 -0.05 -0.08 -0.08 0.23 0.19 0.20 0.15 0.25 0.13 0.23 0.19 0.33 0.22 0.25 0.10 0.23 0.32 0.25 0.32 0.22 -0.34 0.13 -0.06 0.25
Brent Crude 0.25 0.21 0.27 0.34 0.17 0.06 0.19 0.14 0.15 0.20 0.19 0.08 0.07 0.27 0.89 1.00 0.85 0.11 0.62 0.69 0.36 0.34 0.29 0.25 0.20 0.24 0.29 0.27 0.25 -0.17 -0.13 -0.09 -0.14 -0.13 -0.12 -0.10 -0.13 -0.02 -0.12 -0.01 -0.03 -0.08 -0.07 0.23 0.18 0.19 0.16 0.25 0.13 0.24 0.19 0.33 0.22 0.25 0.12 0.23 0.31 0.26 0.32 0.24 -0.34 0.14 -0.05 0.24
Heating Oil 0.22 0.18 0.25 0.31 0.16 0.05 0.17 0.13 0.13 0.18 0.16 0.08 0.07 0.34 0.84 0.85 1.00 0.10 0.64 0.63 0.31 0.30 0.26 0.23 0.18 0.21 0.25 0.24 0.21 -0.14 -0.10 -0.08 -0.11 -0.10 -0.09 -0.08 -0.11 -0.01 -0.09 -0.02 -0.03 -0.06 -0.05 0.19 0.15 0.15 0.13 0.20 0.11 0.21 0.16 0.28 0.18 0.21 0.10 0.20 0.26 0.22 0.28 0.20 -0.30 0.13 -0.03 0.21
Kerosene 0.02 0.00 0.04 0.09 0.02 -0.02 0.02 0.04 0.06 0.03 0.03 0.04 0.04 0.00 0.10 0.11 0.10 1.00 0.28 0.10 0.09 0.10 0.08 0.05 0.14 0.15 0.10 0.08 0.07 -0.03 -0.01 0.00 -0.02 -0.08 -0.06 -0.05 -0.02 -0.14 -0.11 -0.05 0.02 -0.04 -0.02 0.04 0.07 0.09 0.23 0.11 0.01 0.04 0.03 0.08 0.08 0.11 0.33 0.05 0.12 0.11 0.12 0.10 -0.11 0.04 -0.13 0.05
Gas Oil 0.15 0.12 0.18 0.25 0.11 0.02 0.14 0.12 0.15 0.16 0.11 0.08 0.05 0.20 0.56 0.62 0.64 0.28 1.00 0.40 0.29 0.30 0.24 0.19 0.18 0.21 0.25 0.25 0.21 -0.11 -0.07 -0.04 -0.09 -0.10 -0.09 -0.07 -0.09 -0.03 -0.11 -0.01 -0.01 -0.06 -0.04 0.13 0.15 0.16 0.14 0.21 0.08 0.15 0.11 0.19 0.17 0.21 0.09 0.20 0.29 0.23 0.27 0.20 -0.31 0.16 -0.03 0.21
Gasoline 0.25 0.21 0.28 0.37 0.17 0.05 0.19 0.15 0.14 0.19 0.21 0.09 0.09 0.16 0.66 0.69 0.63 0.10 0.40 1.00 0.36 0.34 0.28 0.23 0.21 0.25 0.30 0.27 0.26 -0.18 -0.15 -0.10 -0.16 -0.15 -0.15 -0.15 -0.15 -0.02 -0.14 -0.05 -0.06 -0.11 -0.12 0.26 0.22 0.23 0.18 0.28 0.16 0.26 0.23 0.35 0.25 0.28 0.13 0.19 0.28 0.23 0.31 0.21 -0.31 0.10 -0.08 0.22
Copper NY 0.23 0.21 0.28 0.32 0.20 0.06 0.23 0.19 0.17 0.23 0.18 0.09 0.12 0.10 0.37 0.36 0.31 0.09 0.29 0.36 1.00 0.91 0.45 0.36 0.31 0.39 0.67 0.68 0.57 -0.20 -0.17 -0.13 -0.18 -0.20 -0.19 -0.17 -0.17 -0.06 -0.19 -0.03 -0.06 -0.14 -0.14 0.28 0.36 0.37 0.25 0.40 0.21 0.23 0.26 0.33 0.38 0.38 0.18 0.29 0.35 0.38 0.45 0.29 -0.38 0.20 -0.08 0.32
Copper LDN 0.22 0.21 0.26 0.30 0.18 0.06 0.21 0.18 0.17 0.22 0.16 0.08 0.11 0.09 0.35 0.34 0.30 0.10 0.30 0.34 0.91 1.00 0.42 0.33 0.31 0.39 0.72 0.75 0.60 -0.19 -0.17 -0.12 -0.17 -0.22 -0.20 -0.19 -0.17 -0.06 -0.21 -0.02 -0.06 -0.15 -0.15 0.28 0.38 0.39 0.26 0.43 0.20 0.24 0.26 0.33 0.41 0.41 0.18 0.28 0.35 0.38 0.45 0.28 -0.39 0.18 -0.07 0.33
Silver 0.23 0.20 0.24 0.29 0.17 0.02 0.18 0.20 0.21 0.17 0.18 0.10 0.07 0.08 0.29 0.29 0.26 0.08 0.24 0.28 0.45 0.42 1.00 0.78 0.44 0.51 0.37 0.37 0.29 -0.01 0.02 0.04 0.01 -0.01 0.01 0.01 0.00 0.00 0.00 -0.01 0.06 -0.01 0.00 0.09 0.13 0.13 0.17 0.18 0.04 0.11 0.08 0.23 0.15 0.19 0.12 0.40 0.43 0.40 0.43 0.37 -0.39 0.35 0.14 0.37
Gold 0.18 0.16 0.17 0.23 0.12 0.01 0.13 0.15 0.18 0.13 0.13 0.06 0.02 0.07 0.26 0.25 0.23 0.05 0.19 0.23 0.36 0.33 0.78 1.00 0.43 0.44 0.29 0.30 0.23 0.10 0.12 0.12 0.12 0.11 0.12 0.12 0.10 0.03 0.12 -0.01 0.10 0.07 0.08 -0.02 -0.02 -0.02 0.06 0.04 -0.04 0.01 -0.03 0.14 0.00 0.07 0.05 0.42 0.41 0.35 0.37 0.36 -0.34 0.41 0.23 0.36
Platinum 0.13 0.12 0.17 0.20 0.12 0.05 0.12 0.13 0.13 0.10 0.12 0.06 0.03 0.04 0.20 0.20 0.18 0.14 0.18 0.21 0.31 0.31 0.44 0.43 1.00 0.46 0.30 0.27 0.23 -0.08 -0.06 -0.05 -0.06 -0.09 -0.09 -0.08 -0.06 -0.02 -0.07 0.00 -0.01 -0.07 -0.06 0.12 0.14 0.14 0.15 0.16 0.08 0.13 0.11 0.20 0.16 0.18 0.13 0.24 0.28 0.29 0.33 0.23 -0.27 0.20 0.03 0.27
Palladium 0.17 0.15 0.21 0.24 0.15 0.04 0.16 0.17 0.14 0.15 0.15 0.07 0.06 0.06 0.24 0.24 0.21 0.15 0.21 0.25 0.39 0.39 0.51 0.44 0.46 1.00 0.36 0.36 0.29 -0.11 -0.08 -0.05 -0.09 -0.10 -0.08 -0.06 -0.08 -0.04 -0.09 -0.02 0.00 -0.06 -0.04 0.19 0.21 0.22 0.18 0.26 0.13 0.20 0.17 0.27 0.23 0.27 0.15 0.28 0.32 0.32 0.36 0.25 -0.33 0.22 0.03 0.31
Aluminium 0.20 0.17 0.23 0.27 0.16 0.05 0.19 0.17 0.16 0.19 0.15 0.10 0.10 0.09 0.30 0.29 0.25 0.10 0.25 0.30 0.67 0.72 0.37 0.29 0.30 0.36 1.00 0.68 0.53 -0.16 -0.13 -0.10 -0.14 -0.17 -0.16 -0.15 -0.15 -0.05 -0.16 -0.04 -0.04 -0.13 -0.12 0.23 0.30 0.31 0.18 0.33 0.17 0.20 0.22 0.28 0.32 0.32 0.15 0.27 0.32 0.31 0.36 0.26 -0.34 0.20 -0.04 0.31
Zinc 0.18 0.17 0.21 0.25 0.15 0.07 0.18 0.17 0.16 0.18 0.14 0.07 0.08 0.06 0.27 0.27 0.24 0.08 0.25 0.27 0.68 0.75 0.37 0.30 0.27 0.36 0.68 1.00 0.57 -0.14 -0.14 -0.11 -0.13 -0.16 -0.16 -0.16 -0.14 -0.05 -0.16 -0.03 -0.06 -0.13 -0.12 0.21 0.29 0.30 0.22 0.35 0.15 0.19 0.20 0.26 0.33 0.33 0.16 0.24 0.30 0.31 0.37 0.23 -0.33 0.15 -0.06 0.27
Nickel 0.16 0.14 0.18 0.22 0.13 0.06 0.16 0.15 0.12 0.18 0.12 0.08 0.09 0.05 0.25 0.25 0.21 0.07 0.21 0.26 0.57 0.60 0.29 0.23 0.23 0.29 0.53 0.57 1.00 -0.13 -0.12 -0.09 -0.12 -0.16 -0.13 -0.12 -0.12 -0.04 -0.15 -0.03 -0.05 -0.10 -0.09 0.20 0.26 0.27 0.18 0.30 0.14 0.17 0.19 0.23 0.29 0.27 0.13 0.19 0.24 0.26 0.31 0.18 -0.28 0.13 -0.06 0.23
Treasury Bonds -0.08 -0.10 -0.12 -0.14 -0.08 -0.04 -0.07 -0.06 -0.08 -0.10 -0.09 -0.05 -0.10 -0.02 -0.20 -0.17 -0.14 -0.03 -0.11 -0.18 -0.20 -0.19 -0.01 0.10 -0.08 -0.11 -0.16 -0.14 -0.13 1.00 0.85 0.66 0.93 0.61 0.56 0.46 0.81 0.09 0.54 0.04 0.54 0.33 0.33 -0.35 -0.35 -0.35 -0.12 -0.31 -0.29 -0.31 -0.33 -0.28 -0.34 -0.28 -0.09 0.04 -0.05 -0.09 -0.13 -0.01 0.17 0.15 0.31 -0.09
5 yr T-Notes US -0.07 -0.09 -0.11 -0.12 -0.08 -0.05 -0.06 -0.05 -0.06 -0.10 -0.09 -0.03 -0.11 -0.02 -0.14 -0.13 -0.10 -0.01 -0.07 -0.15 -0.17 -0.17 0.02 0.12 -0.06 -0.08 -0.13 -0.14 -0.12 0.85 1.00 0.90 0.96 0.55 0.57 0.52 0.77 0.09 0.49 0.04 0.76 0.37 0.40 -0.35 -0.35 -0.34 -0.13 -0.30 -0.31 -0.27 -0.33 -0.26 -0.32 -0.25 -0.08 0.11 0.00 -0.05 -0.09 0.04 0.11 0.21 0.34 -0.03
2 yr T-Note US -0.05 -0.07 -0.09 -0.09 -0.07 -0.04 -0.04 -0.03 -0.02 -0.08 -0.07 -0.02 -0.09 -0.02 -0.10 -0.09 -0.08 0.00 -0.04 -0.10 -0.13 -0.12 0.04 0.12 -0.05 -0.05 -0.10 -0.11 -0.09 0.66 0.90 1.00 0.81 0.45 0.50 0.51 0.64 0.07 0.39 0.04 0.85 0.38 0.42 -0.33 -0.31 -0.30 -0.12 -0.27 -0.30 -0.22 -0.30 -0.23 -0.28 -0.21 -0.07 0.15 0.05 -0.02 -0.06 0.08 0.06 0.22 0.31 0.02
10yr T-Notes -0.07 -0.09 -0.11 -0.12 -0.08 -0.04 -0.06 -0.05 -0.07 -0.10 -0.08 -0.04 -0.11 -0.02 -0.17 -0.14 -0.11 -0.02 -0.09 -0.16 -0.18 -0.17 0.01 0.12 -0.06 -0.09 -0.14 -0.13 -0.12 0.93 0.96 0.81 1.00 0.59 0.59 0.51 0.82 0.10 0.53 0.04 0.68 0.36 0.38 -0.35 -0.35 -0.35 -0.12 -0.30 -0.30 -0.28 -0.32 -0.27 -0.33 -0.26 -0.08 0.09 -0.02 -0.06 -0.10 0.02 0.13 0.20 0.34 -0.06
Euro-Bund -0.08 -0.07 -0.11 -0.11 -0.07 -0.04 -0.09 -0.06 -0.10 -0.09 -0.06 -0.06 -0.08 0.00 -0.15 -0.13 -0.10 -0.08 -0.10 -0.15 -0.20 -0.22 -0.01 0.11 -0.09 -0.10 -0.17 -0.16 -0.16 0.61 0.55 0.45 0.59 1.00 0.93 0.76 0.62 0.14 0.81 0.08 0.34 0.49 0.59 -0.30 -0.43 -0.46 -0.16 -0.40 -0.23 -0.27 -0.29 -0.25 -0.45 -0.36 -0.12 -0.02 -0.08 -0.09 -0.13 -0.04 0.17 0.11 0.33 -0.11
Euro-Bobl -0.06 -0.06 -0.10 -0.10 -0.07 -0.03 -0.10 -0.06 -0.09 -0.09 -0.07 -0.06 -0.08 0.00 -0.14 -0.12 -0.09 -0.06 -0.09 -0.15 -0.19 -0.20 0.01 0.12 -0.09 -0.08 -0.16 -0.16 -0.13 0.56 0.57 0.50 0.59 0.93 1.00 0.91 0.59 0.14 0.74 0.08 0.41 0.56 0.73 -0.31 -0.43 -0.46 -0.16 -0.41 -0.25 -0.26 -0.29 -0.25 -0.45 -0.35 -0.12 0.00 -0.05 -0.07 -0.11 -0.02 0.14 0.15 0.33 -0.09
Euro-Schatz -0.08 -0.06 -0.10 -0.11 -0.07 -0.02 -0.09 -0.06 -0.06 -0.10 -0.09 -0.06 -0.07 0.01 -0.12 -0.10 -0.08 -0.05 -0.07 -0.15 -0.17 -0.19 0.01 0.12 -0.08 -0.06 -0.15 -0.16 -0.12 0.46 0.52 0.51 0.51 0.76 0.91 1.00 0.51 0.12 0.59 0.07 0.45 0.59 0.81 -0.29 -0.41 -0.43 -0.16 -0.39 -0.24 -0.22 -0.26 -0.24 -0.42 -0.32 -0.13 0.02 -0.02 -0.06 -0.11 0.00 0.11 0.17 0.30 -0.06
Canadian Bond -0.07 -0.07 -0.09 -0.10 -0.06 -0.04 -0.05 -0.05 -0.07 -0.08 -0.05 -0.07 -0.09 -0.02 -0.15 -0.13 -0.11 -0.02 -0.09 -0.15 -0.17 -0.17 0.00 0.10 -0.06 -0.08 -0.15 -0.14 -0.12 0.81 0.77 0.64 0.82 0.62 0.59 0.51 1.00 0.10 0.55 0.05 0.54 0.34 0.38 -0.34 -0.35 -0.35 -0.11 -0.30 -0.29 -0.29 -0.32 -0.27 -0.34 -0.27 -0.09 0.06 -0.02 -0.07 -0.09 0.00 0.17 0.17 0.30 -0.06
JGB Japan -0.03 -0.02 -0.02 -0.02 -0.02 0.01 0.00 0.00 -0.01 -0.02 -0.02 -0.03 0.01 -0.01 -0.02 -0.02 -0.01 -0.14 -0.03 -0.02 -0.06 -0.06 0.00 0.03 -0.02 -0.04 -0.05 -0.05 -0.04 0.09 0.09 0.07 0.10 0.14 0.14 0.12 0.10 1.00 0.14 0.38 0.06 0.15 0.12 -0.06 -0.09 -0.09 -0.19 -0.10 -0.05 -0.04 -0.06 -0.06 -0.10 -0.11 -0.35 0.03 0.01 -0.06 -0.08 0.00 0.03 0.06 0.08 0.00
Gilts UK -0.06 -0.06 -0.12 -0.13 -0.08 -0.05 -0.08 -0.05 -0.09 -0.08 -0.07 -0.06 -0.10 -0.01 -0.14 -0.12 -0.09 -0.11 -0.11 -0.14 -0.19 -0.21 0.00 0.12 -0.07 -0.09 -0.16 -0.16 -0.15 0.54 0.49 0.39 0.53 0.81 0.74 0.59 0.55 0.14 1.00 0.07 0.28 0.44 0.49 -0.27 -0.38 -0.40 -0.18 -0.37 -0.20 -0.24 -0.26 -0.24 -0.41 -0.33 -0.16 0.02 -0.05 -0.08 -0.12 -0.10 0.16 0.12 0.33 -0.08
Euroyen -0.01 -0.01 -0.02 0.00 -0.01 0.00 0.00 -0.01 -0.03 0.01 -0.01 -0.02 -0.01 0.00 -0.03 -0.01 -0.02 -0.05 -0.01 -0.05 -0.03 -0.02 -0.01 -0.01 0.00 -0.02 -0.04 -0.03 -0.03 0.04 0.04 0.04 0.04 0.08 0.08 0.07 0.05 0.38 0.07 1.00 0.17 0.30 0.25 -0.06 -0.06 -0.06 -0.09 -0.07 -0.05 -0.04 -0.06 -0.07 -0.06 -0.08 -0.17 0.00 0.00 -0.04 -0.06 -0.02 0.03 0.01 0.00 -0.03
Eurodollar -0.01 -0.04 -0.05 -0.04 -0.04 -0.05 -0.01 -0.01 -0.01 -0.06 -0.05 -0.01 -0.07 -0.01 -0.05 -0.03 -0.03 0.02 -0.01 -0.06 -0.06 -0.06 0.06 0.10 -0.01 0.00 -0.04 -0.06 -0.05 0.54 0.76 0.85 0.68 0.34 0.41 0.45 0.54 0.06 0.28 0.17 1.00 0.41 0.48 -0.23 -0.23 -0.21 -0.06 -0.18 -0.23 -0.12 -0.21 -0.17 -0.19 -0.10 -0.03 0.20 0.11 0.03 0.02 0.13 -0.01 0.24 0.26 0.07
Euroswiss -0.05 -0.06 -0.09 -0.08 -0.07 -0.05 -0.04 -0.05 -0.05 -0.07 -0.06 -0.02 -0.08 -0.01 -0.08 -0.08 -0.06 -0.04 -0.06 -0.11 -0.14 -0.15 -0.01 0.07 -0.07 -0.06 -0.13 -0.13 -0.10 0.33 0.37 0.38 0.36 0.49 0.56 0.59 0.34 0.15 0.44 0.30 0.41 1.00 0.69 -0.24 -0.33 -0.33 -0.16 -0.32 -0.20 -0.18 -0.22 -0.20 -0.35 -0.24 -0.17 0.00 -0.05 -0.08 -0.11 -0.03 0.12 0.13 0.21 -0.06
Euribor -0.07 -0.06 -0.09 -0.08 -0.07 -0.04 -0.06 -0.04 -0.05 -0.07 -0.09 -0.04 -0.06 0.00 -0.08 -0.07 -0.05 -0.02 -0.04 -0.12 -0.14 -0.15 0.00 0.08 -0.06 -0.04 -0.12 -0.12 -0.09 0.33 0.40 0.42 0.38 0.59 0.73 0.81 0.38 0.12 0.49 0.25 0.48 0.69 1.00 -0.20 -0.31 -0.32 -0.14 -0.31 -0.18 -0.14 -0.18 -0.19 -0.33 -0.21 -0.15 0.02 -0.01 -0.03 -0.06 0.01 0.06 0.14 0.22 -0.03
SP500 E-Mini 0.14 0.13 0.15 0.20 0.10 0.04 0.11 0.12 0.10 0.17 0.09 0.08 0.12 0.04 0.23 0.23 0.19 0.04 0.13 0.26 0.28 0.28 0.09 -0.02 0.12 0.19 0.23 0.21 0.20 -0.35 -0.35 -0.33 -0.35 -0.30 -0.31 -0.29 -0.34 -0.06 -0.27 -0.06 -0.23 -0.24 -0.20 1.00 0.63 0.61 0.25 0.56 0.84 0.76 0.93 0.73 0.58 0.49 0.16 0.09 0.17 0.26 0.31 0.12 -0.28 -0.06 -0.22 0.22
DAX 30 0.13 0.13 0.17 0.20 0.13 0.04 0.12 0.13 0.11 0.16 0.10 0.08 0.14 0.04 0.19 0.18 0.15 0.07 0.15 0.22 0.36 0.38 0.13 -0.02 0.14 0.21 0.30 0.29 0.26 -0.35 -0.35 -0.31 -0.35 -0.43 -0.43 -0.41 -0.35 -0.09 -0.38 -0.06 -0.23 -0.33 -0.31 0.63 1.00 0.94 0.35 0.81 0.52 0.42 0.59 0.51 0.88 0.64 0.26 0.04 0.16 0.26 0.32 0.10 -0.29 -0.09 -0.26 0.23
Eurostoxx 0.13 0.13 0.17 0.20 0.13 0.06 0.13 0.13 0.12 0.17 0.10 0.09 0.14 0.03 0.20 0.19 0.15 0.09 0.16 0.23 0.37 0.39 0.13 -0.02 0.14 0.22 0.31 0.30 0.27 -0.35 -0.34 -0.30 -0.35 -0.46 -0.46 -0.43 -0.35 -0.09 -0.40 -0.06 -0.21 -0.33 -0.32 0.61 0.94 1.00 0.35 0.86 0.48 0.41 0.57 0.51 0.94 0.65 0.26 0.05 0.19 0.27 0.33 0.11 -0.31 -0.09 -0.28 0.23
Hang Seng 0.08 0.06 0.13 0.19 0.09 0.01 0.08 0.11 0.12 0.09 0.11 0.07 0.08 0.03 0.15 0.16 0.13 0.23 0.14 0.18 0.25 0.26 0.17 0.06 0.15 0.18 0.18 0.22 0.18 -0.12 -0.13 -0.12 -0.12 -0.16 -0.16 -0.16 -0.11 -0.19 -0.18 -0.09 -0.06 -0.16 -0.14 0.25 0.35 0.35 1.00 0.40 0.19 0.19 0.23 0.27 0.38 0.34 0.56 0.10 0.19 0.27 0.34 0.15 -0.21 0.00 -0.15 0.23
FTSE 100 UK 0.16 0.15 0.20 0.25 0.15 0.06 0.15 0.13 0.11 0.18 0.13 0.10 0.14 0.04 0.25 0.25 0.20 0.11 0.21 0.28 0.40 0.43 0.18 0.04 0.16 0.26 0.33 0.35 0.30 -0.31 -0.30 -0.27 -0.30 -0.40 -0.41 -0.39 -0.30 -0.10 -0.37 -0.07 -0.18 -0.32 -0.31 0.56 0.81 0.86 0.40 1.00 0.41 0.42 0.52 0.51 0.89 0.68 0.31 0.10 0.24 0.33 0.40 0.10 -0.34 -0.06 -0.28 0.26
Nasdaq 100 Mini 0.10 0.10 0.11 0.14 0.08 0.01 0.08 0.07 0.06 0.13 0.07 0.06 0.12 0.02 0.13 0.13 0.11 0.01 0.08 0.16 0.21 0.20 0.04 -0.04 0.08 0.13 0.17 0.15 0.14 -0.29 -0.31 -0.30 -0.30 -0.23 -0.25 -0.24 -0.29 -0.05 -0.20 -0.05 -0.23 -0.20 -0.18 0.84 0.52 0.48 0.19 0.41 1.00 0.55 0.71 0.60 0.44 0.34 0.12 0.03 0.09 0.19 0.21 0.06 -0.19 -0.08 -0.15 0.15
Russel 2000 E-Mini 0.12 0.13 0.14 0.19 0.09 0.02 0.11 0.12 0.11 0.16 0.07 0.06 0.10 0.03 0.23 0.24 0.21 0.04 0.15 0.26 0.23 0.24 0.11 0.01 0.13 0.20 0.20 0.19 0.17 -0.31 -0.27 -0.22 -0.28 -0.27 -0.26 -0.22 -0.29 -0.04 -0.24 -0.04 -0.12 -0.18 -0.14 0.76 0.42 0.41 0.19 0.42 0.55 1.00 0.75 0.60 0.43 0.50 0.09 0.15 0.20 0.27 0.29 0.16 -0.28 0.00 -0.21 0.26
Dow Jones 0.11 0.11 0.13 0.18 0.09 0.03 0.08 0.11 0.09 0.15 0.07 0.08 0.11 0.03 0.19 0.19 0.16 0.03 0.11 0.23 0.26 0.26 0.08 -0.03 0.11 0.17 0.22 0.20 0.19 -0.33 -0.33 -0.30 -0.32 -0.29 -0.29 -0.26 -0.32 -0.06 -0.26 -0.06 -0.21 -0.22 -0.18 0.93 0.59 0.57 0.23 0.52 0.71 0.75 1.00 0.66 0.54 0.49 0.14 0.08 0.16 0.24 0.28 0.11 -0.26 -0.06 -0.22 0.20
TSE Toronto 0.18 0.17 0.20 0.24 0.15 0.05 0.13 0.14 0.13 0.18 0.16 0.10 0.10 0.10 0.33 0.33 0.28 0.08 0.19 0.35 0.33 0.33 0.23 0.14 0.20 0.27 0.28 0.26 0.23 -0.28 -0.26 -0.23 -0.27 -0.25 -0.25 -0.24 -0.27 -0.06 -0.24 -0.07 -0.17 -0.20 -0.19 0.73 0.51 0.51 0.27 0.51 0.60 0.60 0.66 1.00 0.51 0.44 0.22 0.13 0.22 0.27 0.32 0.18 -0.24 0.01 -0.16 0.24
CAC 40 France 0.13 0.13 0.18 0.22 0.13 0.06 0.13 0.13 0.13 0.17 0.11 0.08 0.14 0.04 0.22 0.22 0.18 0.08 0.17 0.25 0.38 0.41 0.15 0.00 0.16 0.23 0.32 0.33 0.29 -0.34 -0.32 -0.28 -0.33 -0.45 -0.45 -0.42 -0.34 -0.10 -0.41 -0.06 -0.19 -0.35 -0.33 0.58 0.88 0.94 0.38 0.89 0.44 0.43 0.54 0.51 1.00 0.69 0.30 0.07 0.21 0.30 0.36 0.13 -0.33 -0.08 -0.28 0.25
OMX 30 Stockholm 0.15 0.13 0.20 0.24 0.15 0.04 0.14 0.14 0.14 0.17 0.13 0.11 0.12 0.04 0.25 0.25 0.21 0.11 0.21 0.28 0.38 0.41 0.19 0.07 0.18 0.27 0.32 0.33 0.27 -0.28 -0.25 -0.21 -0.26 -0.36 -0.35 -0.32 -0.27 -0.11 -0.33 -0.08 -0.10 -0.24 -0.21 0.49 0.64 0.65 0.34 0.68 0.34 0.50 0.49 0.44 0.69 1.00 0.26 0.21 0.32 0.36 0.42 0.22 -0.38 0.04 -0.25 0.34
NIKKEI 225 0.05 0.05 0.08 0.12 0.07 0.02 0.08 0.07 0.07 0.05 0.06 0.07 0.04 0.03 0.10 0.12 0.10 0.33 0.09 0.13 0.18 0.18 0.12 0.05 0.13 0.15 0.15 0.16 0.13 -0.09 -0.08 -0.07 -0.08 -0.12 -0.12 -0.13 -0.09 -0.35 -0.16 -0.17 -0.03 -0.17 -0.15 0.16 0.26 0.26 0.56 0.31 0.12 0.09 0.14 0.22 0.30 0.26 1.00 0.06 0.12 0.20 0.26 0.11 -0.15 -0.01 -0.18 0.11
Euro 0.17 0.16 0.17 0.20 0.13 0.00 0.13 0.15 0.21 0.17 0.09 0.06 0.05 0.07 0.23 0.23 0.20 0.05 0.20 0.19 0.29 0.28 0.40 0.42 0.24 0.28 0.27 0.24 0.19 0.04 0.11 0.15 0.09 -0.02 0.00 0.02 0.06 0.03 0.02 0.00 0.20 0.00 0.02 0.09 0.04 0.05 0.10 0.10 0.03 0.15 0.08 0.13 0.07 0.21 0.06 1.00 0.78 0.56 0.58 0.66 -0.48 0.76 0.29 0.57
Norwegian Krone 0.20 0.20 0.22 0.26 0.16 0.01 0.15 0.17 0.22 0.20 0.13 0.05 0.08 0.07 0.32 0.31 0.26 0.12 0.29 0.28 0.35 0.35 0.43 0.41 0.28 0.32 0.32 0.30 0.24 -0.05 0.00 0.05 -0.02 -0.08 -0.05 -0.02 -0.02 0.01 -0.05 0.00 0.11 -0.05 -0.01 0.17 0.16 0.19 0.19 0.24 0.09 0.20 0.16 0.22 0.21 0.32 0.12 0.78 1.00 0.57 0.60 0.61 -0.52 0.60 0.17 0.56
New Zealand Dollar 0.18 0.18 0.19 0.24 0.15 0.01 0.17 0.19 0.22 0.17 0.11 0.07 0.09 0.07 0.25 0.26 0.22 0.11 0.23 0.23 0.38 0.38 0.40 0.35 0.29 0.32 0.31 0.31 0.26 -0.09 -0.05 -0.02 -0.06 -0.09 -0.07 -0.06 -0.07 -0.06 -0.08 -0.04 0.03 -0.08 -0.03 0.26 0.26 0.27 0.27 0.33 0.19 0.27 0.24 0.27 0.30 0.36 0.20 0.56 0.57 1.00 0.82 0.54 -0.56 0.40 0.07 0.56
Australian Dollar 0.21 0.20 0.25 0.30 0.19 0.02 0.20 0.20 0.23 0.21 0.15 0.09 0.11 0.09 0.32 0.32 0.28 0.12 0.27 0.31 0.45 0.45 0.43 0.37 0.33 0.36 0.36 0.37 0.31 -0.13 -0.09 -0.06 -0.10 -0.13 -0.11 -0.11 -0.09 -0.08 -0.12 -0.06 0.02 -0.11 -0.06 0.31 0.32 0.33 0.34 0.40 0.21 0.29 0.28 0.32 0.36 0.42 0.26 0.58 0.60 0.82 1.00 0.54 -0.62 0.40 0.06 0.59
British Pound 0.16 0.15 0.17 0.21 0.12 0.02 0.13 0.15 0.24 0.15 0.10 0.03 0.08 0.06 0.22 0.24 0.20 0.10 0.20 0.21 0.29 0.28 0.37 0.36 0.23 0.25 0.26 0.23 0.18 -0.01 0.04 0.08 0.02 -0.04 -0.02 0.00 0.00 0.00 -0.10 -0.02 0.13 -0.03 0.01 0.12 0.10 0.11 0.15 0.10 0.06 0.16 0.11 0.18 0.13 0.22 0.11 0.66 0.61 0.54 0.54 1.00 -0.46 0.51 0.18 0.48
Canadian Dollar -0.20 -0.20 -0.22 -0.28 -0.17 -0.03 -0.15 -0.17 -0.20 -0.20 -0.06 -0.09 -0.09 -0.10 -0.34 -0.34 -0.30 -0.11 -0.31 -0.31 -0.38 -0.39 -0.39 -0.34 -0.27 -0.33 -0.34 -0.33 -0.28 0.17 0.11 0.06 0.13 0.17 0.14 0.11 0.17 0.03 0.16 0.03 -0.01 0.12 0.06 -0.28 -0.29 -0.31 -0.21 -0.34 -0.19 -0.28 -0.26 -0.24 -0.33 -0.38 -0.15 -0.48 -0.52 -0.56 -0.62 -0.46 1.00 -0.33 -0.03 -0.48
Swiss Franc 0.11 0.12 0.11 0.13 0.08 -0.02 0.09 0.08 0.14 0.11 0.05 0.03 0.01 0.06 0.13 0.14 0.13 0.04 0.16 0.10 0.20 0.18 0.35 0.41 0.20 0.22 0.20 0.15 0.13 0.15 0.21 0.22 0.20 0.11 0.15 0.17 0.17 0.06 0.12 0.01 0.24 0.13 0.14 -0.06 -0.09 -0.09 0.00 -0.06 -0.08 0.00 -0.06 0.01 -0.08 0.04 -0.01 0.76 0.60 0.40 0.40 0.51 -0.33 1.00 0.39 0.45
Japanese Yen -0.02 0.00 -0.01 -0.05 0.01 -0.03 -0.04 0.00 0.01 -0.01 -0.02 -0.03 -0.07 0.01 -0.06 -0.05 -0.03 -0.13 -0.03 -0.08 -0.08 -0.07 0.14 0.23 0.03 0.03 -0.04 -0.06 -0.06 0.31 0.34 0.31 0.34 0.33 0.33 0.30 0.30 0.08 0.33 0.00 0.26 0.21 0.22 -0.22 -0.26 -0.28 -0.15 -0.28 -0.15 -0.21 -0.22 -0.16 -0.28 -0.25 -0.18 0.29 0.17 0.07 0.06 0.18 -0.03 0.39 1.00 0.27
Singapore Dollar 0.17 0.16 0.21 0.23 0.16 0.01 0.16 0.16 0.19 0.17 0.12 0.07 0.09 0.05 0.25 0.24 0.21 0.05 0.21 0.22 0.32 0.33 0.37 0.36 0.27 0.31 0.31 0.27 0.23 -0.09 -0.03 0.02 -0.06 -0.11 -0.09 -0.06 -0.06 0.00 -0.08 -0.03 0.07 -0.06 -0.03 0.22 0.23 0.23 0.23 0.26 0.15 0.26 0.20 0.24 0.25 0.34 0.11 0.57 0.56 0.56 0.59 0.48 -0.48 0.45 0.27 1.00

We see quite high correlations among some of the futures. Does it make sense? Why? Do you see some negative correlations? Do those make sense?

Given such high correlations, we can try to see whether there are some “principal components” (see reading on dimensionality reduction). This analysis can also indicate whether all futures (the global economy!) are driven by some common “factors” (let’s call them “risk factors”).

Variance_Explained_Table_results<-PCA(futures_data, graph=FALSE)
Variance_Explained_Table<-Variance_Explained_Table_results$eig
colnames(Variance_Explained_Table)<-c("Eigenvalue", 
  "Pct of explained variance", "Cumulative pct of explained variance")
Eigenvalue Pct of explained variance Cumulative pct of explained variance
comp 1 14.04 21.94 21.94
comp 2 7.84 12.25 34.19
comp 3 3.52 5.50 39.69
comp 4 3.05 4.77 44.46
comp 5 2.63 4.11 48.57
comp 6 2.38 3.72 52.29
comp 7 2.14 3.34 55.64
comp 8 1.70 2.65 58.29
comp 9 1.46 2.28 60.57
comp 10 1.31 2.04 62.61
comp 11 1.18 1.84 64.45
comp 12 1.14 1.79 66.24
comp 13 1.00 1.56 67.80
comp 14 1.00 1.56 69.36
comp 15 0.98 1.53 70.89
comp 16 0.94 1.47 72.37
comp 17 0.90 1.41 73.78
comp 18 0.87 1.36 75.14
comp 19 0.84 1.32 76.46
comp 20 0.82 1.29 77.75
comp 21 0.79 1.23 78.98
comp 22 0.78 1.22 80.20
comp 23 0.76 1.19 81.39
comp 24 0.70 1.09 82.48
comp 25 0.63 0.98 83.46
comp 26 0.60 0.93 84.40
comp 27 0.59 0.92 85.32
comp 28 0.55 0.86 86.18
comp 29 0.53 0.83 87.01
comp 30 0.51 0.80 87.81
comp 31 0.50 0.78 88.59
comp 32 0.49 0.76 89.35
comp 33 0.45 0.70 90.06
comp 34 0.43 0.67 90.73
comp 35 0.39 0.62 91.34
comp 36 0.38 0.60 91.94
comp 37 0.37 0.57 92.52
comp 38 0.36 0.56 93.07
comp 39 0.35 0.55 93.62
comp 40 0.34 0.53 94.15
comp 41 0.33 0.51 94.67
comp 42 0.32 0.51 95.18
comp 43 0.31 0.48 95.65
comp 44 0.30 0.46 96.12
comp 45 0.29 0.45 96.56
comp 46 0.23 0.36 96.92
comp 47 0.21 0.32 97.24
comp 48 0.20 0.31 97.56
comp 49 0.19 0.30 97.85
comp 50 0.18 0.27 98.13
comp 51 0.16 0.24 98.37
comp 52 0.15 0.24 98.61
comp 53 0.14 0.23 98.84
comp 54 0.13 0.21 99.04
comp 55 0.11 0.16 99.21
comp 56 0.09 0.14 99.35
comp 57 0.09 0.13 99.49
comp 58 0.08 0.13 99.62
comp 59 0.08 0.12 99.74
comp 60 0.06 0.09 99.83
comp 61 0.04 0.06 99.89
comp 62 0.03 0.05 99.94
comp 63 0.02 0.03 99.97
comp 64 0.02 0.03 100.00

Here is the scree plot (see Sessions 3-4 readings):

eigenvalues  <- Variance_Explained_Table[, "Eigenvalue"]

Let’s now see how the 20 first (rotated) principal components look like. Let’s also use the rotated factors (note that these are not really the “principal component”, as explained in the reading on dimensionality reduction) and not show any numbers less than 0.3 in absolute value, to avoid cluttering.

corused = cor(futures_data[, apply(futures_data != 0, 2, sum) > 10, drop = F])
Rotated_Results <- principal(corused, nfactors = 20, rotate = "varimax", score = TRUE)
Rotated_Factors <- round(Rotated_Results$loadings, 2)
Rotated_Factors <- as.data.frame(unclass(Rotated_Factors))
colnames(Rotated_Factors) <- paste("comp", 1:ncol(Rotated_Factors), sep = " ")

sorted_rows <- sort(Rotated_Factors[, 1], decreasing = TRUE, index.return = TRUE)$ix
Rotated_Factors <- Rotated_Factors[sorted_rows, ]
Rotated_Factors[abs(Rotated_Factors) < 0.3] <- NA
comp 1 comp 2 comp 3 comp 4 comp 5 comp 6 comp 7 comp 8 comp 9 comp 10 comp 11 comp 12 comp 13 comp 14 comp 15 comp 16 comp 17 comp 18 comp 19 comp 20
5 yr T-Notes US 0.93
10yr T-Notes 0.93
Treasury Bonds 0.86
2 yr T-Note US 0.85
Canadian Bond 0.79
Eurodollar 0.74 -0.45
Euro-Bund 0.43 0.67 0.44
Euro-Bobl 0.41 0.79
Gilts UK 0.39 0.55 0.47
Euro-Schatz 0.34 0.83
Japanese Yen 0.33 0.36
Euribor 0.87
Euroswiss 0.72
Swiss Franc 0.74
Euro 0.87
Gold 0.34 0.74
Canadian Dollar -0.61
JGB Japan 0.75
British Pound 0.74
Silver 0.32 0.73
Norwegian Krone 0.79
Kerosene 0.87
Sugar 0.67
Coffee 0.64
Orange Juice 0.98
Natural Gas 0.91
Euroyen 0.83
Singapore Dollar 0.70
Corn 0.72
Canola 0.77
NIKKEI 225 0.78
Soybean Meal 0.82
Lean Hoggs 0.99
Gas Oil 0.65 0.40
Platinum 0.69
Soybeans 0.90
Cocoa 0.87
Heating Oil 0.89
Hang Seng 0.78
New Zealand Dollar 0.73
Wheat 0.59 0.36
Soybean Oil 0.74
Brent Crude 0.90
Palladium 0.66
Aluminium 0.77
Zinc 0.81
Nickel 0.72
Gasoline 0.72
Copper LDN 0.84
Australian Dollar 0.72
Cotton 0.73
Lumber 0.98
Crude Oil 0.88
Copper NY 0.79
TSE Toronto 0.71
OMX 30 Stockholm 0.62
FTSE 100 UK 0.81
Russel 2000 E-Mini 0.79
CAC 40 France 0.85
DAX 30 0.82 0.34
Eurostoxx 0.85 0.30
Nasdaq 100 Mini 0.80
Dow Jones 0.85
SP500 E-Mini 0.30 0.89

Questions

  1. How many principal components (“factors”) do we need to explain at least 50% of the variance in this data?
  2. What are the highest weights (in absolute value) of the first principal component portfolio above on the 64 futures?
  3. Can we interpret the first 10 components? How would you call these factors?
  4. Can you now generate the principal components and scree plot using only: a) the pre-crisis bull market years (e.g. only using the data between November 1, 2002, and October 1, 2007)? b) the financial crisis years (e.g. only using the data between October 1, 2007 and March 1, 2009), (Hint: you can select subsets of the data using for example the command crisis_data = futures_data[ as.Date(rownames(futures_data)) > "2007-10-01" & as.Date(rownames(futures_data)) < "2009-03-01" , ])
  5. Based on your analysis in question 3, please discuss any differences you observe about the futures returns during bull and bear markets. What implications may these results have? What do the results imply about how assets are correlated during bear years compared to bull years?

Answers

    1. We need at least 6 components to explain at least 50% of the variance in this data. With these 6 components, we can explain 52.29% of the variance.
    1. The highest weights are 0.93 for both 5 yr T-Notes US and 10yr T-Notes.
    1. Yes, I can interpret the components. Each component is dominantly composed of a group of similar futures, defined by geographies or types. Component 1: North America (US and Canada) bond future performance; Component 2: Major global currencies (Euro, Swiss Franc, British Pound, Norwegian Krone, Singapore Dollar, New Zealand Dollar, Australian Dollar) future performance; Component 3: Major European stock market future performance; Component 4: North America stock market future performance; Component 5: European (EU, UK, Switzerland) bond future performance; Component 6: Oil future performance; Component 7: Non-ferrous metal future performance; Component 8: Soft commodity future performance; Component 9: Precious metal future performance; Component 10: Asian stock market (HK and Japan) future performance
  • 4.1 Bull Market Case
  • 4.1.1 Variance Explained Table
Eigenvalue Pct of explained variance Cumulative pct of explained variance
comp 1 11.19 17.49 17.49
comp 2 8.02 12.53 30.02
comp 3 4.26 6.65 36.67
comp 4 3.55 5.54 42.21
comp 5 3.22 5.02 47.23
comp 6 2.51 3.92 51.16
comp 7 2.16 3.38 54.54
comp 8 1.55 2.41 56.95
comp 9 1.45 2.27 59.22
comp 10 1.37 2.14 61.36
comp 11 1.22 1.90 63.26
comp 12 1.16 1.81 65.06
comp 13 1.06 1.65 66.72
comp 14 1.04 1.63 68.34
comp 15 1.03 1.60 69.95
comp 16 0.99 1.54 71.49
comp 17 0.95 1.48 72.97
comp 18 0.94 1.47 74.45
comp 19 0.90 1.40 75.85
comp 20 0.88 1.37 77.22
comp 21 0.84 1.32 78.54
comp 22 0.81 1.26 79.80
comp 23 0.78 1.22 81.03
comp 24 0.73 1.13 82.16
comp 25 0.71 1.10 83.26
comp 26 0.70 1.10 84.36
comp 27 0.67 1.05 85.41
comp 28 0.65 1.02 86.43
comp 29 0.62 0.96 87.40
comp 30 0.58 0.91 88.31
comp 31 0.55 0.86 89.16
comp 32 0.51 0.79 89.96
comp 33 0.47 0.74 90.69
comp 34 0.43 0.67 91.36
comp 35 0.41 0.64 92.00
comp 36 0.39 0.61 92.61
comp 37 0.38 0.60 93.21
comp 38 0.37 0.58 93.79
comp 39 0.35 0.54 94.33
comp 40 0.34 0.53 94.87
comp 41 0.31 0.48 95.35
comp 42 0.30 0.47 95.82
comp 43 0.28 0.44 96.26
comp 44 0.27 0.43 96.69
comp 45 0.23 0.35 97.04
comp 46 0.22 0.34 97.38
comp 47 0.21 0.32 97.70
comp 48 0.19 0.29 98.00
comp 49 0.17 0.27 98.27
comp 50 0.16 0.26 98.52
comp 51 0.16 0.24 98.77
comp 52 0.15 0.24 99.01
comp 53 0.11 0.17 99.17
comp 54 0.10 0.16 99.33
comp 55 0.08 0.13 99.46
comp 56 0.07 0.11 99.57
comp 57 0.07 0.11 99.68
comp 58 0.05 0.08 99.76
comp 59 0.04 0.07 99.83
comp 60 0.03 0.05 99.88
comp 61 0.03 0.04 99.92
comp 62 0.03 0.04 99.97
comp 63 0.01 0.02 99.99
comp 64 0.01 0.01 100.00
  • 4.1.2 Eigenvalue Plot
  • 4.1.3 Composition of Top 20 Factors
comp 1 comp 2 comp 3 comp 4 comp 5 comp 6 comp 7 comp 8 comp 9 comp 10 comp 11 comp 12 comp 13 comp 14 comp 15 comp 16 comp 17 comp 18 comp 19 comp 20
5 yr T-Notes US 0.94
10yr T-Notes 0.94
2 yr T-Note US 0.91
Treasury Bonds 0.90
Eurodollar 0.85
Canadian Bond 0.81
Euro-Bund 0.47 0.78
Euro-Bobl 0.45 0.81
Euro-Schatz 0.41 0.80
Gilts UK 0.37 0.73
Euribor 0.82
Euroswiss 0.69 0.35
Swiss Franc 0.83
Euro 0.87
Japanese Yen 0.57 -0.35
British Pound 0.80
Norwegian Krone 0.79
JGB Japan -0.47 0.61
Australian Dollar 0.78
Heating Oil 0.92
Orange Juice 0.95
Gasoline 0.48 0.37 -0.30
Silver 0.38 0.32 0.62
Gold 0.49 0.31 0.56
Crude Oil 0.92
Coffee 0.75
Brent Crude 0.91
Natural Gas 0.57
Kerosene 0.92
New Zealand Dollar 0.72
Canadian Dollar -0.59
Singapore Dollar 0.71
Sugar 0.78
Platinum 0.68
Corn 0.54 0.63
Wheat 0.33 0.81
Soybeans 0.93
Soybean Meal 0.84
Gas Oil 0.67 0.33
Copper NY 0.85
Copper LDN 0.90
Euroyen 0.87
Hang Seng 0.74
Soybean Oil 0.81
Lean Hoggs 0.97
Aluminium 0.81
Zinc 0.84
Canola 0.79
Lumber 0.92
Palladium 0.63
Nickel 0.70
Russel 2000 E-Mini 0.86
NIKKEI 225 0.83
TSE Toronto 0.71
Cotton 0.87
OMX 30 Stockholm 0.58 0.36
Cocoa 0.48 0.34 0.35
SP500 E-Mini 0.92
Nasdaq 100 Mini 0.87
Dow Jones 0.88
CAC 40 France 0.84
FTSE 100 UK 0.83
DAX 30 0.78 0.42
Eurostoxx 0.81 0.42
  • 4.2 Crisis Case
  • 4.2.1 Variance Explained Table
Eigenvalue Pct of explained variance Cumulative pct of explained variance
comp 1 19.06 29.78 29.78
comp 2 7.72 12.06 41.84
comp 3 3.87 6.04 47.88
comp 4 3.29 5.15 53.03
comp 5 2.45 3.83 56.85
comp 6 2.17 3.40 60.25
comp 7 2.02 3.16 63.41
comp 8 1.76 2.75 66.16
comp 9 1.48 2.32 68.47
comp 10 1.25 1.95 70.42
comp 11 1.13 1.76 72.19
comp 12 1.07 1.68 73.86
comp 13 1.01 1.57 75.44
comp 14 0.98 1.53 76.97
comp 15 0.89 1.39 78.36
comp 16 0.85 1.32 79.68
comp 17 0.77 1.20 80.88
comp 18 0.74 1.16 82.04
comp 19 0.70 1.09 83.14
comp 20 0.65 1.02 84.16
comp 21 0.63 0.98 85.14
comp 22 0.60 0.93 86.07
comp 23 0.56 0.87 86.94
comp 24 0.54 0.84 87.78
comp 25 0.50 0.78 88.56
comp 26 0.49 0.76 89.32
comp 27 0.46 0.71 90.04
comp 28 0.44 0.69 90.73
comp 29 0.43 0.68 91.41
comp 30 0.42 0.65 92.06
comp 31 0.40 0.62 92.68
comp 32 0.36 0.57 93.25
comp 33 0.34 0.54 93.79
comp 34 0.32 0.50 94.29
comp 35 0.30 0.47 94.76
comp 36 0.29 0.46 95.22
comp 37 0.28 0.43 95.65
comp 38 0.25 0.40 96.05
comp 39 0.23 0.36 96.41
comp 40 0.22 0.34 96.75
comp 41 0.21 0.32 97.07
comp 42 0.20 0.31 97.38
comp 43 0.18 0.29 97.67
comp 44 0.16 0.26 97.92
comp 45 0.15 0.23 98.16
comp 46 0.13 0.21 98.36
comp 47 0.12 0.19 98.55
comp 48 0.11 0.17 98.72
comp 49 0.11 0.17 98.89
comp 50 0.10 0.16 99.05
comp 51 0.08 0.13 99.18
comp 52 0.07 0.11 99.29
comp 53 0.07 0.11 99.40
comp 54 0.06 0.10 99.50
comp 55 0.06 0.09 99.59
comp 56 0.05 0.08 99.67
comp 57 0.05 0.07 99.74
comp 58 0.04 0.07 99.81
comp 59 0.03 0.05 99.86
comp 60 0.03 0.05 99.91
comp 61 0.02 0.03 99.94
comp 62 0.02 0.02 99.97
comp 63 0.01 0.02 99.98
comp 64 0.01 0.02 100.00
  • 4.2.2 Eigenvalue Plot
  • 4.2.3 Composition of Top 20 Factors
comp 1 comp 2 comp 3 comp 4 comp 5 comp 6 comp 7 comp 8 comp 9 comp 10 comp 11 comp 12 comp 13 comp 14 comp 15 comp 16 comp 17 comp 18 comp 19 comp 20
10yr T-Notes 0.93
5 yr T-Notes US 0.91
Treasury Bonds 0.85
2 yr T-Note US 0.84
Eurodollar 0.78 0.33
Canadian Bond 0.72
Japanese Yen 0.38 0.31 -0.33 -0.50
Euro-Bund 0.37 0.75 -0.37
Euro-Bobl 0.33 0.84
Gilts UK 0.33 0.64 -0.43
Euro-Schatz 0.84
Swiss Franc 0.82
Euroswiss 0.74
Euribor 0.87
Gold 0.36 0.78
Euro 0.90
JGB Japan 0.83
Canadian Dollar -0.50 -0.49
Kerosene 0.35 0.80
Silver 0.41 0.73
NIKKEI 225 0.31 0.70 -0.34
Euroyen 0.89
British Pound 0.63 0.38
Palladium 0.57 0.34
Zinc 0.79
Sugar 0.65
Cotton 0.38 0.50
Natural Gas 0.89
Coffee 0.31 0.70
Cocoa 0.35 0.44 0.34
Hang Seng 0.76
Singapore Dollar 0.72
Corn 0.72
Aluminium 0.70
Orange Juice 0.96
Gas Oil 0.49 0.57
Soybean Meal 0.88
Lean Hoggs 0.92
Brent Crude 0.86
Platinum 0.84
New Zealand Dollar 0.63 0.35
Soybeans 0.88
Canola 0.79
Copper LDN 0.77
Soybean Oil 0.72 0.36
Heating Oil 0.84
Gasoline 0.84
Wheat 0.60
Copper NY 0.72
Norwegian Krone 0.78
Australian Dollar 0.54 0.32 0.34
Nickel 0.71
Lumber 0.91
DAX 30 0.35 0.79
Eurostoxx 0.82
FTSE 100 UK 0.78
OMX 30 Stockholm 0.31 0.76
CAC 40 France 0.80
Crude Oil 0.82
TSE Toronto 0.70
Dow Jones 0.91
Russel 2000 E-Mini 0.90
SP500 E-Mini 0.90
Nasdaq 100 Mini 0.89
    1. The order of the components are different for bull and bear markets. For example, the #3 component for bull market is European bond market future vs. soft commodity future in the bear market. #4 component for bull market is non-ferrous metal future vs. North America stock market future for the bear market. #5 component for bull market is oil market future vs. European bond market future in the bear market. There are also differences in other top 20 factors as well. Compared with the analysis from question 3, we can see that commodities such as oil and non-ferrous metals seem to outperform in bull market as they have higher eigenvalues compared to the overall case and the bear market case. On the other hand, soft commodities seem to be closely correlated with the bear market. Additionally, the eigenvalues of top factors are also different in the bull and bear market cases. In the bull market case, variance explained seems to be more evenly distributed among factors, whereas in the bear market case, the #1 factor along accounts for almost 30% of variance explained. The performance of North America bond market future seems to be a good indicator for the arrival of the bear market.

A Simple Futures Trend Following Strategy

We can now develop a simple futures trend following trading strategy, as outlined in the papers in the Exercise Introduction above. There are about $300 billion invested in such strategies! Of course we cannot develop here a sophisticated product, but with some more work…

We will do the following:

  1. Calculate a number of moving averages of different “window lengths” for each of the 64 futures - there are many so called technical indicators one can use. We will use the “moving average” function ma for this (try for example to see what this returns ma(1:10,2) ).
  2. Add the signs (can also use the actual moving average values of course - try it!) of these moving averages (as if they “vote”), and then scale this sum across all futures so that the sum of their (of the sum across all futures!) absolute value across all futures is 1 (hence we invest $1 every day - you see why?).
  3. Then invest every day in each of the 64 an amount that is defined by the weights calculated in step 2, using however the weights calculated using data until 2 days ago (why 2 days and not 1 day?) - see the use of the helper function shift for this.
  4. Finally see the performance of this strategy.

Here is the code:

signal_used = 0 * futures_data  # just initialize the trading signal to be 0
# Take many moving Average (MA) Signals and let them 'vote' with their sign
# (+-1, e.g. long or short vote, for each signal)
MAfreq <- seq(10, 250, by = 20)
for (iter in 1:length(MAfreq)) signal_used = signal_used + sign(apply(futures_data, 
    2, function(r) ma(r, MAfreq[iter])))
# Now make sure we invest $1 every day (so the sum of the absolute values of
# the weights is 1 every day)
signal_used = t(apply(signal_used, 1, function(r) {
    res = r
    if (sum(abs(r)) != 0) 
        res = r/sum(abs(r))
    res
}))
colnames(signal_used) <- colnames(futures_data)
# Now create the returns of the strategy for each futures time series
strategy_by_future <- scrub(shift(signal_used, 2) * futures_data)  # signal 2 days ago
# finally, this is our futures trend following strategy
trading_strategy = apply(strategy_by_future, 1, sum)
names(trading_strategy) <- rownames(futures_data)

Reporting the performance results

Let’s see how this strategy does:

Here is how this strategy has performed during this period:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year
2001 0.61 1.55 1.81 -2.00 0.54 0.69 0.75 1.35 4.30 0.33 -2.26 -2.45 5.13
2002 0.20 -0.44 -2.61 1.01 0.39 1.72 2.06 1.65 3.38 -2.50 -1.27 3.07 6.64
2003 2.39 3.37 -2.85 -0.92 1.25 -1.25 0.73 -0.13 -0.33 4.23 0.10 3.10 9.86
2004 1.22 3.16 0.06 -1.66 -0.13 -1.40 3.00 -2.75 4.36 -0.77 0.98 -0.07 5.91
2005 -0.55 1.03 0.27 -2.03 -0.27 0.84 0.42 1.51 0.25 -1.05 2.17 0.30 2.86
2006 2.00 -0.87 2.05 3.85 -0.30 -1.63 -0.76 0.00 0.60 2.23 0.50 1.17 9.05
2007 0.13 -0.52 -0.96 1.69 0.01 0.77 -0.90 -1.28 3.15 1.81 -0.05 1.98 5.88
2008 2.52 5.71 -3.06 0.36 2.38 4.06 -4.41 -1.66 5.35 14.30 3.88 1.61 34.20
2009 1.23 2.07 -5.43 -2.20 -0.82 -0.93 1.92 3.00 0.12 0.39 2.02 0.91 2.01
2010 -3.39 0.19 3.88 1.10 -5.04 -2.45 -1.27 0.01 2.31 3.59 -1.06 6.41 3.75
2011 1.27 2.48 -1.58 2.63 -4.07 -2.15 0.58 -0.77 1.23 -4.67 0.63 -0.38 -5.01
2012 -0.94 0.20 0.34 -0.12 1.57 -1.80 1.35 -0.33 -0.74 -0.92 -0.36 0.13 -1.65
2013 1.29 -0.58 1.07 0.15 1.29 0.52 0.51 -0.72 0.14 0.42 1.29 0.44 5.96
2014 -1.12 0.80 -0.11 0.54 -0.41 -0.16 0.69 0.96 0.89 0.52 2.53 2.64 7.98
2015 1.77 -0.73 1.63 -2.32 0.39 -0.43 1.50 -1.70 1.17 1.18

How does this compare with existing CTA products such as this one from Societe Generale? (Note: one can easily achieve a correlation of more than 0.8 with this specific product - as well as with many other ones)

Compare our strategy with this product

Compare our strategy with this product

Questions

  1. What does the command “MAfreq<-seq(10,250,by=20)” in the code above do? How is MAfreq used later?
  2. What happens if you use different parameters for this command? Please explore and report below the returns (monthly and yearly returns, as in the example above) of a trading strategy you build by modifying the parameters.

Answers

    1. This command defines the “window lengths” of moving average used later. The lengths come as a arithmetic sequence starting from 10 with 20 as incremental value. Then it is used in later iteration process to compute different lengths of moving average signals to determine the long / short positions for the signals.
  • 2.1 “MAfreq2<-seq(10,30,by=5)”
  • In this case, we are using much shorter historical time period for the moving average computation. The results we get are more volatile than the results from the original functions. Return during the financial crisis for 2008 is 39.3% vs. 34.2% in the original case. However, when the stock market is gradually recovering after the financial crisis, the new strategy underperforms even more, -13.9% for 2011 vs. -5.0% in the original case. Total cumulative return as of September 2015 is less than 50% vs. 92% in the original case.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year
2001 0.53 0.94 2.05 -1.01 0.24 0.20 1.76 0.17 3.84 0.38 0.03 -2.04 7.20
2002 -3.06 -1.53 2.48 -0.47 0.75 1.90 1.75 -0.47 2.41 -1.54 1.00 1.13 4.26
2003 0.68 2.55 -3.64 0.16 2.01 0.44 1.23 -0.82 1.29 0.51 -1.88 1.81 4.24
2004 0.78 1.82 -0.56 -2.08 1.38 -1.67 2.47 -1.46 1.51 -0.93 0.82 -0.74 1.21
2005 -2.48 1.70 0.51 -1.62 -0.21 0.42 -0.13 2.67 -0.59 0.22 1.70 0.14 2.24
2006 0.83 -1.10 0.51 3.89 0.02 -1.84 -3.25 0.94 0.73 0.94 1.03 -1.35 1.19
2007 -0.36 0.24 0.65 2.34 -0.93 0.79 -0.24 0.05 2.96 1.38 0.55 -0.57 6.98
2008 2.26 4.64 -2.55 0.10 1.68 1.67 -0.80 3.23 4.45 14.52 1.47 3.87 39.33
2009 -4.68 -1.37 -3.16 4.38 4.45 -1.24 -1.61 0.93 -2.42 -0.92 0.74 -0.83 -5.97
2010 -0.58 -2.48 2.29 0.62 0.22 -1.45 0.03 -1.04 1.29 2.78 -1.62 1.69 1.60
2011 -1.12 0.45 -1.62 1.91 -5.26 -1.16 -1.23 -0.46 1.74 -3.59 -4.10 -0.18 -13.91
2012 0.95 1.95 -1.02 -0.59 4.71 -1.65 1.06 0.57 0.46 -1.42 -1.20 0.20 3.93
2013 0.95 -0.97 0.64 -0.18 1.19 0.10 -1.44 -1.09 -1.19 -0.55 -0.33 0.23 -2.66
2014 -1.70 0.63 -0.42 -1.21 -0.28 -0.27 1.91 0.06 1.26 -0.12 1.65 1.66 3.14
2015 2.33 0.53 -2.37 -0.75 -2.38 -0.56 0.80 -0.03 1.21 -1.30
  • 2.2 “MAfreq3<-seq(10,310,by=40)”
  • In this case, we are using longer historical time period for the moving average computation. The results slightly underperform the original case in bull market from 2002-2004 but slightly outperform from 2005-2007. In recent bull market from 2013-2015, the new method also slightly outperform the original case. However, when volatility is high in 2008 and 2009, this case underperform the original case. Overall return is slightly below 92% at 86%. The original selection of parameters is quite optimal.
Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year
2001 0.61 1.76 0.68 -2.04 0.29 0.29 0.51 0.64 4.20 0.48 -2.25 -2.72 2.28
2002 0.46 -0.63 -2.99 0.82 0.56 1.94 2.19 1.52 3.34 -2.50 -1.58 3.37 6.45
2003 2.32 3.21 -2.80 -0.85 0.89 -1.60 0.09 -0.12 0.21 4.01 -0.05 3.50 8.91
2004 0.81 3.06 0.19 -1.62 0.25 -1.34 2.91 -2.52 4.13 -0.63 1.16 -0.46 5.86
2005 -0.55 1.04 0.19 -1.95 -0.28 0.71 0.35 1.82 0.24 -1.02 2.17 0.70 3.40
2006 2.21 -0.94 2.25 3.55 -0.48 -1.12 -1.08 0.39 0.59 1.91 0.56 1.00 9.08
2007 0.38 -0.57 -0.58 1.88 0.00 0.45 -0.88 -0.99 3.06 1.82 -0.31 2.05 6.37
2008 2.61 6.29 -2.82 0.44 2.16 4.41 -4.34 -1.95 4.40 13.11 3.85 1.99 33.21
2009 1.35 2.32 -5.36 -2.68 -3.69 -1.32 1.43 3.23 -0.09 -0.25 1.99 0.90 -2.52
2010 -3.39 0.30 4.06 1.18 -4.97 -1.75 -1.03 -0.15 2.78 3.65 -0.87 6.23 5.59
2011 1.17 2.49 -1.55 2.77 -3.49 -2.34 0.87 -1.11 -0.66 -3.89 0.40 -0.83 -6.24
2012 -0.98 0.35 0.11 -0.09 1.90 -2.25 1.32 -0.23 -1.39 -0.45 -0.11 0.17 -1.71
2013 1.31 -0.43 1.03 0.49 1.43 0.28 0.96 -0.73 0.21 0.21 1.47 0.42 6.83
2014 -1.06 1.01 0.08 0.49 -0.35 0.05 0.65 1.10 0.98 0.82 2.63 2.38 9.08
2015 1.87 -0.54 1.57 -1.98 0.40 -0.38 1.89 -1.76 0.92 1.92

Further explorations (Optional)

Now you have seen how to develop some trading strategies that hedge funds have been using for centuries. Clearly this is only the very first step - as many of the online resources on technical indicators also suggest. Can you now explore more such strategies? How good a futures trend following hedge fund strategy can you develop?

Here is for example something that can be achieved relatively easily…

Here is how this strategy has performed during this period:

Jan Feb Mar Apr May Jun Jul Aug Sep Oct Nov Dec Year
2001 0.00 0.00 0.68 -1.00 0.02 -0.05 0.60 0.95 2.41 1.25 -2.21 -0.98 1.59
2002 -0.56 -0.18 -0.81 0.21 1.09 1.92 1.85 1.25 1.75 -0.93 -0.68 2.76 7.85
2003 1.33 1.53 -0.83 0.12 1.86 -0.90 -0.31 -0.20 -0.03 1.98 0.09 1.82 6.58
2004 0.76 1.90 -0.07 -1.83 -0.19 -0.32 0.33 -1.02 1.32 0.19 1.33 0.26 2.62
2005 -0.36 0.37 0.02 -0.70 0.51 0.93 0.13 0.17 0.69 -0.04 1.55 0.41 3.72
2006 1.21 -0.04 2.10 2.03 -0.42 -0.17 -0.89 -0.54 -0.15 0.95 0.71 0.73 5.61
2007 0.39 -0.98 -0.08 1.70 1.18 1.33 -1.27 -2.41 2.01 1.11 0.29 0.67 3.92
2008 2.60 2.96 -0.98 -0.37 0.69 1.68 -1.97 -0.14 1.78 4.35 1.62 0.73 13.57
2009 0.05 0.72 -1.36 -1.15 0.41 -0.73 0.88 0.83 0.71 -0.14 1.64 -0.63 1.19
2010 -1.26 0.47 1.34 0.77 -1.30 -0.49 -0.45 1.10 1.04 1.67 -0.89 2.38 4.38
2011 0.58 1.16 -0.69 1.74 -1.71 -1.50 0.98 0.64 0.81 -1.86 0.46 0.39 0.93
2012 -0.29 -0.15 -0.05 -0.10 1.27 -1.08 0.66 -0.25 -0.22 -0.77 -0.18 -0.13 -1.31
2013 1.09 -0.98 0.82 -0.03 0.72 0.85 0.20 -0.26 0.12 0.23 0.90 1.01 4.73
2014 -1.33 0.46 -0.12 0.06 0.32 0.42 0.01 1.15 1.85 0.68 2.07 1.49 7.24
2015 2.17 -0.30 1.10 -1.49 0.27 0.04 0.40 -0.77 0.73 2.11